| 1. | It is based on the Generalized Langevin Equation ( GLE ).
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| 2. | On small timescales, inertial effects are prevalent in the Langevin equation.
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| 3. | In physics, however, stochastic integrals occur as the solutions of Langevin equations.
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| 4. | However, the Langevin equation is more general.
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| 5. | On long timescales, the mathematical Brownian motion is well described by a Langevin equation.
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| 6. | In those cases, the Langevin equation, which looks at particle acceleration, must be used.
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| 7. | The equipartition theorem can be used to derive the Brownian motion of a particle from the Langevin equation.
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| 8. | The " Langevin equation " describes advection, diffusion, and other phenomena in an explicitly stochastic way.
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| 9. | In 1991, he derived, with Bedeaux, the Langevin equation for a Brownian particle using only causality and time reversal invariance.
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| 10. | In the white noise setting described so far, the quantum Langevin equation for an arbitrary system operator a takes a simpler form:
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